Example 4.3: Model 3 The SEIRS Multi species Spatial

The SEIRS spatial model with two species

As same as the Example 3, but we suppose the population consists of two species human and bird. The system of ODEs that represents the whole model after being integrated with three concerns: SEIRS, multi-species and spatial concerns.

Kendrick Script

KendrickModel SEIRS
    attribute: #(status -> S E I R);
    parameters: #(beta lambda gamma mu sigma nu);
    lambda: #(beta*I/N);
    transitions: #(
        S -- lambda --> E.
        E -- sigma --> I.
        I -- gamma --> R.
        R -- nu --> S.
        status -- mu --> Empty.
        Empty -- mu --> S.).

KendrickModel MultiSpecies
    attribute: #(species -> humans birds).

KendrickModel MetaPopulation
    attribute: #(zone -> 1 2 3 4 5)
    parameters: #(rho);
    connectionMatrix: #(
      #(0 1 0 0 0)
      #(0 0 1 0 0)
      #(0 0 0 1 0)
      #(0 0 0 0 1)
      #(1 0 0 0 0)
    );
    transitionRate: #(rho).

Composition Influenza
    model: 'SEIRS';
    model: 'MultiSpecies';
    model: 'MetaPopulation'.

Scenario Scr1
    on: 'Influenza';
    populationSize: 27500;
    mu_species: #(0.000365 0.00137);
    beta_species_species: #(#(0 0.21) #(0 0.42));
    gamma_species: #(0.25 0.233);
    sigma_species: #(0.5 0.67);
    nu: 0.00274;
    rho_species: #(0.03 0.1);
    lambda: #(beta*I_zone/N sum);
    N: #(species_zone);
    S_humans: 2500;
    S_birds: 25000;
    S_birds_1: 4990;
    I_birds_1: 10.

Simulation InfluenzaSim rungeKutta
    scenario: 'Scr1';
    from: 0;
    to: 550;
    step: 1.

Visualization InfluenzaViz diagram
    for: 'InfluenzaSim';
    data: #(I_species);
    legendTitle: 'Infectious';
    legends: #('humans' 'birds');
    xLabel: 'Time (days)'.